Had the same problem, ended up spending like 2 hours searching. Finally, found it though, it's contained in a chest, much like the chest at the save points. Check the second floor of a warehouse outside of Thieve's Landing town proper. It's in the office of the warehouse. Now I just have to take a bounty alive and I'll have that outfit. As a sidenote, I have to say that the duster is my favorite outfit so far.

There is a scrap of the outfit available for sale from the tailor, but that is not the piece needed for the search checkmark.

I don't get why people aren't specific. The scrap you need to find is located in a chest on the second floor of the warehouse that has two smoker vents with smog coming out. If you are coming from the south through Stillwater Creek on the main road into Thieves Landing, look to your right as soon as you get near the exclamation point for the taxi stage coat. You will see the warehouse.